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Continuous representations of the meta Hahn algebra and special functions
Quentin Labriet, Luc Vinet
Infinite families of biorthogonal rational functions are constructed using infinite dimensional representations of the three-generated meta Hahn algebra. Continuous Hahn and contin…
Para families of orthogonal polynomials
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Krawtchouk polynomials arose in the search for spin chains with perfect state transfer; the para-Racah, -para-Racah and para-Bannai--Ito polynomials followed, obtained…
The supersymmetric Scarf I Hamiltonian with reflections and its discrete para-Bannai--Ito version
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Bannai--Ito polynomials are orthogonal on a Bannai--Ito bi-lattice that is \emph{two-sided} --- it extends on both sides of a central value --- and depend, besides t…
The para--Racah Hamiltonian as an exactly solvable discretization of the Pöschl--Teller box
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Racah polynomials, taken at the persymmetric value of their isospectral deformation parameter, define through their recurrence relation a mirror-symmetric tridiagonal Hami…
The para--Krawtchouk oscillator and its continuum limit
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Krawtchouk polynomials define, through their recurrence relation, a finite oscillator model that exhibits fractional revival. We determine the continuum limit of this Hami…
Universal scaling of spatially extended zero modes in inhomogeneous SSH chains
Gilles Parez, Nicolas Crampé, Quentin Labriet +2
Protected zero modes are a hallmark of topological phases of matter and are exponentially localized at sharp interfaces between distinct gapped phases. We investigate how this pict…
Algebraic Leonard trio approach to rational functions: the Hahn case
Nicolas Crampé, Quentin Labriet, Lucia Morey +1
The finite families of Hahn polynomials and associated biorthogonal rational functions are interpreted algebraically in the framework of Leonard trios. We introduce the trio Hahn a…
The dynamical algebra of the generic superintegrable model on the two-sphere
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
The rank two Jacobi algebra is identified as the dynamical algebra of the generic quadratic superintegrable model on the two-sphere. The physical representation of…
Meta Algebras and Special Functions: the Racah Case
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
Finite families of biorthogonal rational functions and orthogonal polynomials of Racah-type are studied within a unified algebraic framework based on the meta Racah algebra and its…
Exceptional theta correspondences via Plancherel formulas for rank one symmetric spaces
Jan Frahm, Quentin Labriet
We consider the minimal representation of (a finite cover of) the conformal group of a simple split Jordan algebra over or , whenever it exists. The confor…
Bispectral rational functions and Leonard trios
Nicolas Crampé, Wolter Groenevelt, Quentin Labriet +3
It is well-known that Leonard pairs have a close connection with bispectral orthogonal polynomials of the Askey scheme. In this paper, we introduce the notion of a Leonard trio $(V…